Write as many expressions as you can that have the same value as 10 to the 6 power. Focus on using
exponents and multiplication.

Answer:

21) 7(2x+3y)

22) 16(2x+3y)

Answer:

A.32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

the formula for circumference is 2πr. Using math we get r as 32

Answer:

see explanation

Step-by-step explanation:

I don't have graphing facilities but can give you the vertex and 1 other point.

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

x = - \(\frac{b}{2a}\)

y = - x² - 2x + 8 ← is in standard form

with a = - 1 and b = - 2 , then

x = - \(\frac{-2}{-2}\) = - 1

Substitute x = - 1 into the equation for corresponding value of y

y = - (- 1)² - 2(- 1) + 8 = - 1 + 2 + 8 = 9

vertex = (- 1, 9 )

To obtain another point substitute any value for x into the equation

x = 0 : y = 0 - 0 + 8 , then (0, 8 ) is a point on the graph

x = 2 : y = - (2)² - 2(2) + 8 = - 4 - 4 + 8 = 0  then (2, 0 ) is a point on the graph

The total cost of the program is $1,000, we divide this by the number of impressions (in thousands) to get the CPM. Thus, the CPM is $1,000 / 10,000 = $0.10.

The CPM (Cost Per Thousand) can be calculated by dividing the total cost of the program by the number of impressions (in thousands). In this case, the program has a women rating of 20, meaning it reaches 20% of the target population, which is 500,000 women.

To calculate the number of impressions, we multiply the target population by the women rating and divide by 1,000. The CPM is then obtained by dividing the total cost by the number of impressions (in thousands).

To calculate the number of impressions, we multiply the target population (500,000) by the women rating (20%) and divide by 1,000. This gives us (500,000 * 20) / 1,000 = 10,000 impressions.

Since the total cost of the program is $1,000, we divide this by the number of impressions (in thousands) to get the CPM. Thus, the CPM is $1,000 / 10,000 = $0.10.

Therefore, the given answer choices are not correct as none of them match the calculated CPM of $0.10.

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Probability of an event is the measure of its chance of occurrence. The correct probabilities are:

Suppose that the sample space is S. Out of which there are two events, A and B, subsets of S.

Then, we can interpret P(A|B) as the probability of that part of A which is in B, with the new sample space as B. (assuming probabililty of B isn't 0).

Symbolically, we write it as:

\(P(A|B) = \dfrac{P(A \cap B)}{P(B)}\)

For three sets, A, B and C:

\(n(A \cup B \cup C) = n(A) + P(B) + P(C) - n(A\cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)\)

The problem is incomplete. The corresponding venn diagram is attached below.

We can symbolize the venn diagram as:

\(n(A) = 12+8+6+5 =31\\n(B) = 11+8+5+3 = 27\\n(C) = 4+8+6+3 = 21\\n(A \cap B) = 5+8=13\\n(B\cap C) = 3+8=11\\n(A \cap C) = 6+8=14\\n(A \cap B \cap C) = 8\)

S = sample space = collection of all unique elements.

S is union of A, B and C.

\(n(S) = n(A \cup B\cup C) = 31 + 27 + 21 -13-11-14+8 = 49\)

Checking all the options for their correctness:

We have:

\(P(A|C) = P(A\cap C)/P(C) = \dfrac{n(A\cap C)/n(S)}{n(C)/n(S)} = \dfrac{n(A \cap C)}{n(C)} = \dfrac{14}{21} =\dfrac{2}{3}\)

Thus, its correct.

\(P(C|B) = P(C\cap B)/P(B) = \dfrac{n(C\cap B)/n(S)}{n(B)/n(S)} = \dfrac{n(C \cap B)}{n(B)} = \dfrac{11}{27} \neq \dfrac{8}{27}\)

Thus, this option is incorrect.

Thus, this option is incorrect.

\(P(C) = \dfrac{n(C)}{n(S)}= \dfrac{21}{49} =\dfrac{3}{7}\)

Thus, its correct.

\(P(B|A) = P(B\cap A)/P(A) = \dfrac{n(B\cap A)/n(S)}{n(A)/n(S)} = \dfrac{n(B\cap A)}{n(A)} = \dfrac{13}{31} \neq \dfrac{13}{27}\)

Thus, this option is incorrect.

Thus, the correct probabilities are:

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The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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Answer:

20.36 is the answer

2.12x3=6.36

3.50x4=14

14+6.36=20.36

Answer:

20.36

Step-by-step explanation:

1)3*2.12=6.36

2)4*3.50=14

3)6.36+14=20.36

Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

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Answer:

95°

Step-by-step explanation:

y° = 180° - (55° + 30°)

y° = 180° - 85°

y ° = 95°

y = 95

x = y ( vertical angles)

x = 95°

Answer:0.5j^27+3j+168.45

Step-by-step explanation: I used a calculator

Answer: its C because when you put it in order you should easily find it in the question. So, 1, 2, 3, 4, 5, 6, 9, 12, 15 is the full order but C is the closest answer to the question. Hope its right!

Answer:

how many O's u would use would be 4

Step-by-step explanation:

Answer:

Timmy ate 13/24 of the pizza.

Step-by-step explanation:

To solve this problem, first you need to know how much pizza Jack and John ate. We know that Jack ate 1/4 of the pizza, and that John ate half of that, so we know that John ate 1/8 of the pizza. Together, Jack and John ate (1/4 + 1/8), which equals 3/8 of a pizza. Next, we need to find how much of the pizza Timmy ate. We know that he has eaten 1/6 more of the pizza than Jack and John combined, so that would be 1/6 more than 3/8. To add 1/6 to 3/8, we need to have a common denominator. The lowest common denominator would be 24, so you would have 4/24 + 9/24. That equals 13/24, so we know that Timmy ate 13/24 of the pizza.

the answer will be:

36-x = 3(4+x)

Answer:B

Step-by-step explanation:

2.45(0.35)= 0.8575+2.45= 3.30

Answer:

v = -24

Step-by-step explanation:

7/8 v = -21

Multiply each side by 8/7 to isolate b

8/7 * 7/8 v = -21 * 8/7

v = -24

Answer:

L,KMKOMJIUN8IUJJNUJJMJIKM

Step-by-step explanation:

the probabilities for each event are Red ball: 1/5, White ball: 7/20, Yellow ball: 9/20 by using formula of  probability =possible outcome /total outcomes

To find the probability of a given event, we need to determine the number of successful outcomes and divide that by the total number of possible outcomes.

In this case, the event we want to find the probability for is not specified, so I will provide the probabilities for each color:

1. Probability of drawing a red ball:

Number of successful outcomes: 4 red balls
Total number of outcomes: 4 red + 7 white + 9 yellow = 20 balls

Probability of drawing a red ball = (Number of red balls) / (Total number of balls) = 4/20 = 1/5

2. Probability of drawing a white ball:

Number of successful outcomes: 7 white balls

Probability of drawing a white ball = (Number of white balls) / (Total number of balls) = 7/20

3. Probability of drawing a yellow ball:

Number of successful outcomes: 9 yellow balls

Probability of drawing a yellow ball = (Number of yellow balls) / (Total number of balls) = 9/20

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The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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Answer:

31.42

Step-by-step explanation:

radius= half diameter

circumfrence= 2pi*r

you would do pi times 5

Answer:

Step-by-step explanation:

1.x +y = 1   Yes

2. Power of variable e is 3. So, it is not a linear equation

No.

3) Great than symbol is there. No, it is not a linear equation.

4. 2x -y = 2x + 5

2x - y - 2x = 5

      -y = 5 is not a linear equation with two variable.

No.

5. No.

1) (5,14)  ; (19,7)

\(Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{7-14}{19-5}\\\\=\dfrac{-7}{14}\\\\=\dfrac{-1}{2}\)

2) (-10 , 1)  ; (-10 ,4)

x- coordinate is same for both the points. So, the line is parallel to y-axis

Slope = undefined

\(3) (-3,-3) ; (15,13)\\\\slope=\dfrac{13-[-3]}{15-[-3]}\\\\=\dfrac{13+3}{15+3}\\\\=\dfrac{16}{18}\\\\=\dfrac{8}{9}\)

\(4)(\dfrac{-1}{2},\dfrac{1}{7}) ; (\dfrac{-3}{2},\dfrac{2}{7})\\\\Slope=\dfrac{\dfrac{2}{7}-\dfrac{1}{7}}{\dfrac{-3}{2}+\dfrac{1}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{\dfrac{-2}{2}}\\\\\\=\dfrac{\dfrac{1}{7}}{-1}\\\\\\=\dfrac{-1}{7}\)

Compare with y = mx + b  ; here m is slope

1. y = -2x - 8

slope = -2

2. x = 3

Line is parallel to y-axis.

So, slope = undefined

3.2x - y = 4

        2x - 4 = y

y = 2x - 4

Slope = 2

4.) 2x + y - 5 = 0

       y = -2x + 5

Slope = -2

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

Equation and solution of equation :

17.25 + p(17.50) = 69.75

17.25 + 17.50p = 69.75

17.50x = 69.75 - 17.25

17.50p = 52.50

p = 52.50/17.50

p = 3

So three people can go to the amusement park (assuming that they are all travelling together in the same car).

The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

A group of friends wants to go to the amusement park. they have $69.75 to spend on parking and admission. Parking is $17.25, and tickets cost $17.50 per person, including tax.

Let p be the number of people. Then the equation is given as,

17.50p + 17.25 = 69.75

The equation that represents the number of people who can go to the amusement park will be 17.50p + 17.25 = 69.75.

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Answer:

  (smallest, largest) = (B, C), (D, E), (G, J)

Step-by-step explanation:

Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

__

The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.

The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.

The shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.

_____

Additional comment

Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there cannot be two angles in a triangle such that the smaller angle has the larger sine.

Answer:

.002 or

2x10^-3

Step-by-step explanation:

make sure the exponents match

8 x 10^-3 =

.008 × 10^-3

(.008 × 10^-6) ÷ (4 x 10^-6)

10^-6 cancels out

.008 ÷ 4 = .002

or

2x10^-3

There are 70 ways to choose 4 shoes from the pile of 8.

We can apply the combination formula, which is: to select 4 shoes from the pile of 8:

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

where n is the total number of shoes (8) and k is the number of shoes we want to choose (4).

Substituting the values, we get:

\({ }^8 C_4=\frac{8!}{4!*(8-4)!}=\frac{8*7*6*5}{4*3*2*1} =70\)

Therefore, there are 70 ways to choose 4 shoes from the pile of 8.

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The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

ap e x

Step-by-step explanation:

66

The answer for Exactly 5 successes of at most 1 success is 0.8650

We can use the binomial distribution to solve these problems. For a binomial distribution with n trials and probability of success p, the probability of getting exactly k successes is:

P(k) = (n choose k) * \(p^k\)* (1-p)(n-k)

where (n choose k) = n! / (k!(n-k)!) is the binomial coefficient.

For the given experiment with n=8 and p=3/8:

a. To find the probability of exactly 5 successes:

P(5) = (8 choose 5) * (3/8)\(.^5\) * (5/8)\(.^3\)

= 0.1014 (rounded to four decimal places)

b. To find the probability of at least 7 successes:

P(at least 7) = P(7) + P(8)

= (8 choose 7) * (3/8)\(.^7\) * (5/8)\(.^1\) + (8 choose 8) * (3/8)\(.^8\) * (5/8)\(.^0\)

= 0.0056 + 0.0000

= 0.0056

c. To find the probability of at most 1 success:

P(at most 1) = P(0) + P(1)

= (8 choose 0) * (3/8)\(.^0\) * (5/8)\(.^8\) + (8 choose 1) * (3/8)\(.^1\) * (5/8)\(.^7\)

= 0.8650

Therefore, the answers are:

a. 0.1014

b. 0.0056

c. 0.8650

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To solve this problem, we will use the binomial probability formula: P(x) = (n choose x) * p^x * (1-p)^(n-x). The answer is e) 0.1350.

where n is the number of trials, x is the number of successes we want to find the probability of, p is the probability of success on each trial, and (n choose x) is the binomial coefficient, which represents the number of ways we can choose x successes out of n trials.

a. To find the probability of exactly 5 successes, we have:

P(5) = (8 choose 5) * (3/8)^5 * (5/8)^3
P(5) = 56 * 0.0105 * 0.2373
P(5) = 0.0304

Therefore, the answer is a) 0.0304.

b. To find the probability of at least 7 successes, we can use the complement rule: P(at least 7) = 1 - P(6 or fewer).

P(6 or fewer) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6)
P(6 or fewer) = (8 choose 0) * (3/8)^0 * (5/8)^8 + (8 choose 1) * (3/8)^1 * (5/8)^7 + ... + (8 choose 6) * (3/8)^6 * (5/8)^2
P(6 or fewer) = 0.9897

Therefore, P(at least 7) = 1 - 0.9897 = 0.0103

Therefore, the answer is e) 0.0311.

c. To find the probability of at most 1 success, we can add up the probabilities of getting 0 successes and 1 success:

P(0 or 1) = P(0) + P(1)
P(0 or 1) = (8 choose 0) * (3/8)^0 * (5/8)^8 + (8 choose 1) * (3/8)^1 * (5/8)^7
P(0 or 1) = 0.0506 + 0.0844
P(0 or 1) = 0.1350

Therefore, the answer is e) 0.1350.

In an experiment with 8 independent trials and a probability of success of 3/8 on each trial, the probability of obtaining exactly 5 successes is approximately 0.1014 (option b). The probability of obtaining at least 7 successes is approximately 0.0056 (option a), and the probability of obtaining at most 1 success is approximately 0.1350 (option e).

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